Details

Time bar (total: 18.3s)

analyze1.8s (9.8%)

Algorithm
search
Search
TrueOtherFalseIter
0%99.9%0.1%0
0%99.9%0.1%1
0%99.9%0.1%2
0%99.9%0.1%3
0%99.9%0.1%4
0%99.9%0.1%5
0%99.9%0.1%6
0%99.9%0.1%7
25%74.9%0.1%8
54.6%45.2%0.1%9
56.2%43.7%0.1%10
62.4%37.4%0.1%11
65.9%33.9%0.1%12
66.3%33.5%0.1%13
69%30.8%0.1%14
Compiler

Compiled 20 to 15 computations (25% saved)

sample8.6s (47%)

Results
6.7s4807×body1024valid
1.1s1451×body512valid
381.0ms1439×body128valid
293.0ms551×body256valid
19.0msbody2048valid
Compiler

Compiled 59 to 44 computations (25.4% saved)

simplify82.0ms (0.4%)

Algorithm
egg-herbie
Rules
645×associate-/r*_binary64
634×sqr-pow_binary64
394×associate-*l*_binary64
373×cube-prod_binary64
368×*-commutative_binary64
Counts
1 → 2
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
01426
12618
24018
36818
414118
534818
6105518
7179618
8248418
9269718
10296818
11331118
12370518
13460318
14479918

prune4.0ms (0%)

Pruning

3 alts after pruning (3 fresh and 0 done)

PrunedKeptTotal
New022
Fresh011
Picked000
Done000
Total033
Error
0.2b
Counts
3 → 2
Alt Table
StatusErrorProgram
0.2b
(*.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx))) (sin.f64 th))
3.5b
(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))) (sin.f64 th))
Compiler

Compiled 96 to 63 computations (34.4% saved)

localize9.0ms (0%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.0b
(sin.f64 ky)
0.1b
(hypot.f64 (sin.f64 ky) (sin.f64 kx))
0.1b
(/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx)))
0.2b
(*.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx))) (sin.f64 th))

series344.0ms (1.9%)

Counts
4 → 88
Calls

4 calls:

190.0ms
(*.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx))) (sin.f64 th))
125.0ms
(/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx)))
26.0ms
(hypot.f64 (sin.f64 ky) (sin.f64 kx))
2.0ms
(sin.f64 ky)

rewrite15.0ms (0.1%)

Algorithm
rewrite-expression-head
Rules
25×add-sqr-sqrt_binary64
20×*-un-lft-identity_binary64
20×add-cube-cbrt_binary64
19×times-frac_binary64
13×associate-*l*_binary64
Counts
4 → 82
Calls

4 calls:

6.0ms
(*.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx))) (sin.f64 th))
3.0ms
(/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx)))
1.0ms
(sin.f64 ky)
0.0ms
(hypot.f64 (sin.f64 ky) (sin.f64 kx))

simplify207.0ms (1.1%)

Algorithm
egg-herbie
Rules
539×cancel-sign-sub-inv_binary64
308×fma-neg_binary64
224×sub-neg_binary64
206×fma-def_binary64
164×*-commutative_binary64
Counts
170 → 199
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
03354685
19304356
232354356
348634352
449904352
549974352
649994352
749544352

prune205.0ms (1.1%)

Pruning

8 alts after pruning (8 fresh and 0 done)

PrunedKeptTotal
New2088216
Fresh101
Picked101
Done000
Total2108218
Error
0b
Counts
218 → 8
Alt Table
StatusErrorProgram
24.8b
(cbrt.f64 (*.f64 (*.f64 (*.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx))) (sin.f64 th)) (*.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx))) (sin.f64 th))) (*.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx))) (sin.f64 th))))
1.4b
(/.f64 (*.f64 (sin.f64 ky) (sin.f64 th)) (hypot.f64 (sin.f64 ky) (sin.f64 kx)))
31.3b
(*.f64 (*.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx))) (sqrt.f64 (sin.f64 th))) (sqrt.f64 (sin.f64 th)))
6.6b
(*.f64 (/.f64 (sin.f64 ky) (cbrt.f64 (pow.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) 3))) (sin.f64 th))
0.3b
(*.f64 (/.f64 1 (/.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)) (sin.f64 ky))) (sin.f64 th))
0.8b
(*.f64 (/.f64 1 (sqrt.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)))) (*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)))) (sin.f64 th)))
0.4b
(*.f64 (/.f64 (sin.f64 ky) (expm1.f64 (log1p.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx))))) (sin.f64 th))
1.3b
(*.f64 (/.f64 (*.f64 (cbrt.f64 (sin.f64 ky)) (cbrt.f64 (sin.f64 ky))) 1) (*.f64 (/.f64 (cbrt.f64 (sin.f64 ky)) (hypot.f64 (sin.f64 ky) (sin.f64 kx))) (sin.f64 th)))
Compiler

Compiled 5767 to 2186 computations (62.1% saved)

localize11.0ms (0.1%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.1b
(hypot.f64 (sin.f64 ky) (sin.f64 kx))
0.2b
(/.f64 1 (/.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)) (sin.f64 ky)))
0.2b
(*.f64 (/.f64 1 (/.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)) (sin.f64 ky))) (sin.f64 th))
0.2b
(/.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)) (sin.f64 ky))

series415.0ms (2.3%)

Counts
3 → 84
Calls

3 calls:

243.0ms
(*.f64 (/.f64 1 (/.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)) (sin.f64 ky))) (sin.f64 th))
122.0ms
(/.f64 1 (/.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)) (sin.f64 ky)))
50.0ms
(/.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)) (sin.f64 ky))

rewrite36.0ms (0.2%)

Algorithm
rewrite-expression-head
Rules
156×times-frac_binary64
103×add-sqr-sqrt_binary64
91×*-un-lft-identity_binary64
89×add-cube-cbrt_binary64
44×associate-*l*_binary64
Counts
3 → 181
Calls

3 calls:

10.0ms
(*.f64 (/.f64 1 (/.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)) (sin.f64 ky))) (sin.f64 th))
5.0ms
(/.f64 1 (/.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)) (sin.f64 ky)))
2.0ms
(/.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)) (sin.f64 ky))

simplify174.0ms (1%)

Algorithm
egg-herbie
Rules
453×cancel-sign-sub-inv_binary64
256×associate-*r*_binary64
232×fma-def_binary64
219×sub-neg_binary64
203×*-commutative_binary64
Counts
265 → 344
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
03697707
110017004
236716977
349596977

prune341.0ms (1.9%)

Pruning

7 alts after pruning (7 fresh and 0 done)

PrunedKeptTotal
New3743377
Fresh347
Picked101
Done000
Total3787385
Error
0b
Counts
385 → 7
Alt Table
StatusErrorProgram
24.8b
(cbrt.f64 (*.f64 (*.f64 (*.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx))) (sin.f64 th)) (*.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx))) (sin.f64 th))) (*.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx))) (sin.f64 th))))
1.4b
(/.f64 (*.f64 (sin.f64 ky) (sin.f64 th)) (hypot.f64 (sin.f64 ky) (sin.f64 kx)))
31.3b
(*.f64 (*.f64 (/.f64 1 (/.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)) (sin.f64 ky))) (sqrt.f64 (sin.f64 th))) (sqrt.f64 (sin.f64 th)))
1.5b
(*.f64 (/.f64 1 (hypot.f64 (sin.f64 ky) (sin.f64 kx))) (*.f64 (sin.f64 ky) (sin.f64 th)))
0.8b
(*.f64 (/.f64 1 (sqrt.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)))) (*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)))) (sin.f64 th)))
0.4b
(*.f64 (/.f64 (sin.f64 ky) (expm1.f64 (log1p.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx))))) (sin.f64 th))
0.6b
(*.f64 (/.f64 1 (*.f64 (sqrt.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky))) (/.f64 (sqrt.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky))) (sin.f64 ky)))) (sin.f64 th))
Compiler

Compiled 10722 to 3888 computations (63.7% saved)

localize12.0ms (0.1%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.1b
(/.f64 (sin.f64 ky) (expm1.f64 (log1p.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)))))
0.2b
(log1p.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)))
0.2b
(*.f64 (/.f64 (sin.f64 ky) (expm1.f64 (log1p.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx))))) (sin.f64 th))
0.3b
(expm1.f64 (log1p.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx))))

series1.3s (7.3%)

Counts
4 → 108
Calls

4 calls:

995.0ms
(log1p.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)))
196.0ms
(*.f64 (/.f64 (sin.f64 ky) (expm1.f64 (log1p.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx))))) (sin.f64 th))
118.0ms
(/.f64 (sin.f64 ky) (expm1.f64 (log1p.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)))))
28.0ms
(expm1.f64 (log1p.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx))))

rewrite16.0ms (0.1%)

Algorithm
rewrite-expression-head
Rules
25×add-sqr-sqrt_binary64
20×*-un-lft-identity_binary64
20×add-cube-cbrt_binary64
19×times-frac_binary64
13×associate-*l*_binary64
Counts
4 → 85
Calls

4 calls:

5.0ms
(*.f64 (/.f64 (sin.f64 ky) (expm1.f64 (log1p.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx))))) (sin.f64 th))
3.0ms
(/.f64 (sin.f64 ky) (expm1.f64 (log1p.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)))))
1.0ms
(expm1.f64 (log1p.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx))))
0.0ms
(log1p.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)))

simplify127.0ms (0.7%)

Algorithm
egg-herbie
Rules
295×sub-neg_binary64
278×fma-def_binary64
251×times-frac_binary64
238×associate-/r*_binary64
207×associate-/l*_binary64
Counts
193 → 221
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
04225770
112085276
244665273
350325273

prune172.0ms (0.9%)

Pruning

7 alts after pruning (6 fresh and 1 done)

PrunedKeptTotal
New2210221
Fresh066
Picked011
Done000
Total2217228
Error
0b
Counts
228 → 7
Alt Table
StatusErrorProgram
24.8b
(cbrt.f64 (*.f64 (*.f64 (*.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx))) (sin.f64 th)) (*.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx))) (sin.f64 th))) (*.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx))) (sin.f64 th))))
1.4b
(/.f64 (*.f64 (sin.f64 ky) (sin.f64 th)) (hypot.f64 (sin.f64 ky) (sin.f64 kx)))
31.3b
(*.f64 (*.f64 (/.f64 1 (/.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)) (sin.f64 ky))) (sqrt.f64 (sin.f64 th))) (sqrt.f64 (sin.f64 th)))
1.5b
(*.f64 (/.f64 1 (hypot.f64 (sin.f64 ky) (sin.f64 kx))) (*.f64 (sin.f64 ky) (sin.f64 th)))
0.8b
(*.f64 (/.f64 1 (sqrt.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)))) (*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)))) (sin.f64 th)))
0.4b
(*.f64 (/.f64 (sin.f64 ky) (expm1.f64 (log1p.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx))))) (sin.f64 th))
0.6b
(*.f64 (/.f64 1 (*.f64 (sqrt.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky))) (/.f64 (sqrt.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky))) (sin.f64 ky)))) (sin.f64 th))
Compiler

Compiled 6915 to 2742 computations (60.3% saved)

localize13.0ms (0.1%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.2b
(/.f64 1 (*.f64 (sqrt.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky))) (/.f64 (sqrt.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky))) (sin.f64 ky))))
0.2b
(*.f64 (/.f64 1 (*.f64 (sqrt.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky))) (/.f64 (sqrt.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky))) (sin.f64 ky)))) (sin.f64 th))
0.2b
(/.f64 (sqrt.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky))) (sin.f64 ky))
0.3b
(*.f64 (sqrt.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky))) (/.f64 (sqrt.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky))) (sin.f64 ky)))

series436.0ms (2.4%)

Counts
4 → 108
Calls

4 calls:

196.0ms
(*.f64 (/.f64 1 (*.f64 (sqrt.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky))) (/.f64 (sqrt.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky))) (sin.f64 ky)))) (sin.f64 th))
118.0ms
(/.f64 1 (*.f64 (sqrt.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky))) (/.f64 (sqrt.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky))) (sin.f64 ky))))
70.0ms
(/.f64 (sqrt.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky))) (sin.f64 ky))
52.0ms
(*.f64 (sqrt.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky))) (/.f64 (sqrt.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky))) (sin.f64 ky)))

rewrite43.0ms (0.2%)

Algorithm
rewrite-expression-head
Rules
64×add-exp-log_binary64
57×add-sqr-sqrt_binary64
46×times-frac_binary64
39×*-un-lft-identity_binary64
39×add-cube-cbrt_binary64
Counts
4 → 164
Calls

4 calls:

9.0ms
(*.f64 (/.f64 1 (*.f64 (sqrt.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky))) (/.f64 (sqrt.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky))) (sin.f64 ky)))) (sin.f64 th))
8.0ms
(*.f64 (sqrt.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky))) (/.f64 (sqrt.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky))) (sin.f64 ky)))
8.0ms
(/.f64 1 (*.f64 (sqrt.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky))) (/.f64 (sqrt.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky))) (sin.f64 ky))))
3.0ms
(/.f64 (sqrt.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky))) (sin.f64 ky))

simplify183.0ms (1%)

Algorithm
egg-herbie
Rules
341×fma-def_binary64
324×associate-*r*_binary64
238×associate-*l*_binary64
225×fma-neg_binary64
208×associate-/l*_binary64
Counts
272 → 308
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
04758457
113027478
247997478
349657478

prune229.0ms (1.3%)

Pruning

7 alts after pruning (5 fresh and 2 done)

PrunedKeptTotal
New3071308
Fresh145
Picked011
Done011
Total3087315
Error
0b
Counts
315 → 7
Alt Table
StatusErrorProgram
24.8b
(cbrt.f64 (*.f64 (*.f64 (*.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx))) (sin.f64 th)) (*.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx))) (sin.f64 th))) (*.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx))) (sin.f64 th))))
1.4b
(/.f64 (*.f64 (sin.f64 ky) (sin.f64 th)) (hypot.f64 (sin.f64 ky) (sin.f64 kx)))
1.5b
(*.f64 (/.f64 1 (hypot.f64 (sin.f64 ky) (sin.f64 kx))) (*.f64 (sin.f64 ky) (sin.f64 th)))
31.2b
(*.f64 (/.f64 (sqrt.f64 (sin.f64 th)) (/.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)) (sin.f64 ky))) (sqrt.f64 (sin.f64 th)))
0.8b
(*.f64 (/.f64 1 (sqrt.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)))) (*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)))) (sin.f64 th)))
0.4b
(*.f64 (/.f64 (sin.f64 ky) (expm1.f64 (log1p.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx))))) (sin.f64 th))
0.6b
(*.f64 (/.f64 1 (*.f64 (sqrt.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky))) (/.f64 (sqrt.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky))) (sin.f64 ky)))) (sin.f64 th))
Compiler

Compiled 10598 to 3516 computations (66.8% saved)

regimes3.4s (18.4%)

Accuracy

Total 0.2b remaining (80.1%)

Threshold costs 0.2b (80.1%)

Counts
299 → 1
Compiler

Compiled 55339 to 35870 computations (35.2% saved)

simplify2.0ms (0%)

Algorithm
egg-herbie
Rules
*-commutative_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01018
11118
21118

end121.0ms (0.7%)

Compiler

Compiled 180 to 98 computations (45.6% saved)

Profiling

Loading profile data...